Learning embeddings of non-linear PDEs: the Burgers' equation
Embeddings provide low-dimensional representations that organize complex function spaces and support generalization. They provide a geometric representation that supports efficient retrieval, comparison, and generalization. In this work we generalize the concept to Physics Informed Neural Networks. We present a method to construct solution embedding spaces of nonlinear partial differential equations using a multi-head setup, and extract non-degenerate information from them using principal component analysis (PCA). We test this method by applying it to viscous Burgers' equation, which is solved simultaneously for a family of initial conditions and values of the viscosity. A shared network ...
| Authors | Pedro Tarancón-Álvarez, Leonid Sarieddine, Pavlos Protopapas et al. |
|---|---|
| Primary category | math.AP |
| Published | 8 March 2026 |
| Last updated at source | 8 March 2026 |
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